A quadratic C0 interior penalty method for the quad-curl problem

Abstract

In this paper we study the C0 interior penalty method for a quad-curl problem arising from magnetohydrodynamics model on bounded polygons or polyhedrons. We prove the well-posedness of the numerical scheme and then derive the optimal error estimates in a discrete energy norm. A post-processing procedure that can produce C1 approximations is also presented. The performance of the method is illustrated by numerical experiments.

Keywords

• C0 interior penalty method
• MHD
• quad-curl problem
• error analysis